When parallel lines are cut by a transversal, why are same-side interior angles supplementary? Use the fact that a line parallel to the transversal can be drawn to form a parallelogram in your answer.

A because the sum of the measures of a pair of same-side interior angles is equal to one-fourth the number of degrees in a parallelogram

B because the sum of the measures of a pair of same-side interior angles is equal to one-half the number of degrees in a parallelogram

C because the sum of the measures of a pair of same-side interior angles is equal to the number of degrees in a parallelogram

D because the sum of the measures of a pair of same-side interior angles is equal to twice the number of degrees in a parallelogram

Question

Mathematics

Lina Owens

3 October, 23:21

When parallel lines are cut by a transversal, why are same-side interior angles supplementary? Use the fact that a line parallel to the transversal can be drawn to form a parallelogram in your answer.

A because the sum of the measures of a pair of same-side interior angles is equal to one-fourth the number of degrees in a parallelogram

B because the sum of the measures of a pair of same-side interior angles is equal to one-half the number of degrees in a parallelogram

C because the sum of the measures of a pair of same-side interior angles is equal to the number of degrees in a parallelogram

D because the sum of the measures of a pair of same-side interior angles is equal to twice the number of degrees in a parallelogram

+4

Answers (1)

Know the Answer?

Emely Osborne · Answer 1

Because the sum of the measures of a pair of same-side interior angles

is equal to one-half the number of degrees in a parallelogram ⇒ B

Step-by-step explanation:

* Lets explain how to solve the problem

- In a parallelogram every two opposite sides are parallel

- In a parallelogram every tow opposite angles are equal

∵ The parallelogram is a quadrilateral

∵ The sum of the measures of the interior angles in any quadrilateral

is 360°

∵ In parallelogram each two opposite angles are equal

∴ The sum of the measures of every two adjacent angles

equal 360° : 2 = 180°

* Lets solve the problem

- When parallel lines are cut by a transversal

∵ It is a fact that the parallel lines and their transversal can form a

parallelogram

∵ The sum of the measures of the adjacent angles of the

parallelogram is 180°

∵ The sum of the measures of the supplementary angles is 180°

∴ The same side-interior angles are supplementary, because

they are two adjacent angles in a parallelogram

* Lets find the true statement

∵ The sum of the measures of every two adjacent interior angles

in the parallelogram = 360° : 2 = 180°

∵ 180° is half the sum of the measures of interior angles in the

parallelogram

∴ Because the sum of the measures of a pair of same-side interior

angles is equal to one-half the number of degrees in a

parallelogram